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Wave equation least square imaging using the local angular Hessian for amplitude correction
Author(s) -
Ren Haoran,
Wu RuShan,
Wang Huazhong
Publication year - 2011
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.2011.00947.x
Subject(s) - hessian matrix , wavenumber , computation , amplitude , mathematical analysis , inversion (geology) , mathematics , geometry , algorithm , physics , optics , geology , paleontology , structural basin
Local angular Hessian can be used to improve wave equation least square migration images. By decomposing the original Hessian operator into the local wavenumber domain or the local angle domain, the least square migration image is obtained as the solution of a linearized least‐squares inversion in the frequency and local angle domains. The local angular Hessian contains information about the acquisition geometry and the propagation effects based on the given velocity model. The inversion scheme based on the local angular Hessian avoids huge computation on the exact inverse Hessian matrix. To reduce the instability in the inversion, damping factors are introduced into the deconvolution filter in the local wavenumber domain and the local angle domain. The algorithms are tested using the SEG/EAGE salt2D model and the Sigsbee2A model. Results show improved image quality and amplitudes.